Question

find value of x
(x-7)(x-8)=(x-5)(x-4)​

Answer 1

Answer:-

$\large{\underline{\boxed{\sf x = 6}}}$

Explanation:-

Given equation ;

$\sf (x - 7)(x - 8) = (x - 5)(x - 4) \\ \\ \implies \sf x {}^{2} - 7x - 8x + 56 = {x}^{2} - 5x - 4x + 20 \\ \\ \implies \sf {x}^{2} - 15x + 56 = x {}^{2} - 9x + 20 \\ \\ \implies \sf x {}^{2} - 15x + 56 - x {}^{2} + 9x - 20 = 0 \\ \\ \implies \sf -6x + 36 = 0 \\ \\ \implies \sf -6x = - 36 \\ \\\implies \sf x = \frac{36}{6}\\\\ \boxed{ \bf \therefore \: x = 6 }$

Verification:-

(x - 7)(x - 8) = (x - 5)(x - 4)

⇒ (6 - 7)(6 - 8) = (6 - 5)(6 - 4)

⇒ - 1 * (-2) = 1 * 2

⇒ 2 = 2

∴ LHS = RHS

_______________________

Hence, the answer is 6.

Answer 2

Explanation:

(x-7)(x-8)=(x-5)(x-4)

x(x-8)-7(x-8)=x(x-4)-5(x-4)

x.x-8x-7x+56=x.x-4x-5x+20

-8x-7x+56=-4x-5x+20

-15x+56=-9x+20

56-20=-9x+15x

36=6x

x=6